Scanning probe microscopes are a class of imaging techniques in which a tip that interacts locally with a sample is scanned over the surface of the sample to generate a three-dimensional image representing the properties of the surface. For example, in atomic force microscopy, the surface interaction force between the probe tip and the sample are measured at each point on the sample. The tip has a very small end and is mounted on the end of a cantilevered arm. As the tip is moved over the surface of the sample, the arm deflects in response to the changes in topology of the surface. The vertical position of the cantilever arm relative to the sample is adjusted to maintain the arm in a predetermined state. The vertical position as a function of position on the sample can then be used to provide an image of the surface.
Images are typically acquired in one of two modes. In the contact or constant force mode, the tip is brought into contact with the sample and the tip moves up and down as the tip is moved over the surface. The deflection of the arm is a direct measure of force and topographical variations. A feedback controller measures the deflection and adjusts the height of the probe tip so as to maintain constant force between the cantilevered probe and the surface, i.e., the arm at a fixed deflection. This mode of operation can subject the sample being imaged to excessive shear forces that can alter or damage the sample. This limitation is particularly acute when biological samples or macromolecules are being imaged.
Accordingly, some form of AC mode of scanning is often preferred for these applications. In the AC, or dynamic mode, the tip and arm are oscillated at a frequency near the resonant frequency of the arm. The height of the tip can be controlled such that the tip avoids contact with the sample surface, sampling short-range tip/sample forces. Alterations in the oscillation parameters from short range forces between the tip and the sample result in changes in the oscillations of the tip. Alternatively, the tip can be allowed to make light intermittent contact with the sample only at the bottom of the oscillation cycle. Contact between the probe tip and the sample results in an alteration of the amplitude, phase and/or frequency of the oscillation. The controller adjusts the height of the probe over the sample such that the oscillation amplitude, phase and/or frequency is kept at a predetermined constant value. Since the tip is not in constant contact with the sample, the shear force applied to the sample is significantly less than in the mode in which the tip is in constant contact. For soft samples, this mode reduces the damage that the tip can inflict on the sample and also provides a more accurate image of the surface in its non-disturbed configuration.
The image is constructed one point at a time and is limited by the rate at which the tip can be moved relative to the sample, as well as the time required for the servo loop to reposition the tip vertically to maintain the distance between the surface and the tip. The feedback control system that is used to position the arm vertically over the sample must extract the needed information from the oscillatory signal provided by the system that tracks the position of the tip as a function of time. The process of extracting the information from the oscillating signal will be referred to as demodulation in the following discussion.
When a demodulated error signal is used in a feedback control loop, a significant delay is incurred in the generation of the error signal. The delay reflects the time needed to extract the information from the signal. This time is typically many periods of the oscillation of the signal. This delay results in a phase lag in the feedback loop, and hence, reduces the speed with which the feedback loop can adjust to changes in the oscillatory signal.
In AC mode, the time needed to detect a change in one or more of the oscillatory parameters of the arm is many periods of the oscillation. Hence, each time the position of the arm is moved relative to the sample, the servo system must wait for a period of time that is long compared to the oscillation period to determine the new amplitude, phase, or frequency of the oscillation and then alter the distance between the arm and the surface to return the oscillatory parameter of interest to the desired value. As a result, the time needed to provide an image can be excessive.